Sherwood number estimation

Cybulski and Moulijn [27] proposed an experimental method for simultaneous determination of kinetic parameters and mass transfer coefficients in washcoated square channels. The model parameters are estimated by nonlinear regression, where the objective function is calculated by numerical solution of balance equations. However, the method is applicable only if the structure of the mathematical model has been identified (e.g., based on literature data) and the model parameters to be estimated are not too numerous. Otherwise the estimates might have a limited physical meaning. The method was tested for the catalytic oxidation of CO. The estimate of effective diffusivity falls into the range that is typical for the washcoat material (y-alumina) and reacting species. The Sherwood number estimated was in between those theoretically predicted for square and circular ducts, and this clearly indicates the influence of rounding the comers on the external mass transfer. 

The authors reported that Eq. (28) describes the experimental results of their own and those from other research groups well. The Sherwood number estimated from Eq. (28) is plotted against Rep in Fig. 4... 

The Sherwood number, Sh, is estimated from Table 16-9, and the dispersion parameters Yi and Jo ffom Table 16-10 for well-packed columns. Typical values are a 1-4 and b 0.5-1. Since HETP -2HTU, Fig. 16-13 can also be used for approximate calculations. 

The second approach to estimating source strength is also provided by the USGS (1984) and utilizes what is referred to as the Sherwood number and the Peclet number ... 

The designer now needs to make some estimates of mass transfer. These properties are generally well known for commercially available adsorbents, so the job is not difficult. We need to re-introduce the adsorber cross-section area and the gas velocity in order to make the required estimates of the external film contribution to the overall mass transfer. For spherical beads or pellets we can generally employ Eq. (7.12) or (7.15) of Ruthven s text to obtain the Sherwood number. That correlation is the mass transfer analog to the Nusselt number formulation in heat transfer ... 

This is simply the definition of the mass transfer coefficient km, the subject of mass transfer courses is to find suitable correlations in order to estimate k A (units of lengthAime). The mass transfer coefficient is in turn defined through the Sherwood number,... 

Because D is independently determined, and p is obtainable from initial conditions and thermod5mamic equilibrium, the problem of determining the convective dissolution rate now becomes the problem of estimating the boundary layer thickness. In fluid dynamics, the boundary layer thickness appears in a dimensionless number, the Sherwood number Sh ... 

The liquid-solid mass transfer coefficient was estimated from the correlation provided by Temkin et al. (14). The method is based on the estimation of Sherwood number (Sh), starting from Reynolds (Re) and Schmidt (Sc) numbers. 

In a recent overview, Iliuta et al. [59] proposed a new correlation, which estimates the liquid Sherwood number with an average absolute relative error of 22.3% and a standard deviation of 25.3%. 

The nonlinear least squares regression program PEST [79] was used to fit the proposed correlation relating the time invariant Sherwood number to overall Peclet numbers for circular pools given by Eq. (91) to the seven experimentally determined Sh values presented in Fig. 12b, in order to estimate the empirical coefficients fi, y2> and y3. The experimental, overall Sherwood number correlation applicable to circular TCE pool dissolution in water saturated, homogeneous porous media can be expressed by the following relationship ... 

The moderate and low Peclet numbers correspond to cases where all terms of eq. (2) are significant and numerical solution is required. A non-uniform finite-difference discretization schema has been chosen for solving the boundary value problem of eq. (1) with boundary conditions (3a-e), estimating the overall Sherwood number, Sho, as follows ... 

Solution of a reactor problem in the mass transfer limit requires an estimation of the appropriate mass transfer coefficient. Fortunately, mass transfer correlations have been developed to aid the determination of mass transfer coefficients. For example, the Sherwood number, Sh, relates the mass transfer coefficient of a species A to its diffusivity and the radius of a catalyst particle, Rp ... 

In both BSR modules, the Sherwood number lies between the two Chilton-Colbum predictions, as expected. The most important conclusion to be drawn from these graphs, is that the Sherwood number for turbulent flow in a BSR can be predicted with an accuracy of ca. 30% (which is usually acceptable) on the basis of one single pressure drop experiment in the turbulent-flow regime. From this pressure experiment the empirical roughness function can be fitted, with which the friction factor can be adequately predicted as a function of Re, as discussed in the previous section from these an upper estimate of Sh... 

In order to characterize mass transfer in the boundary layers, it is necessary to determine the respective mass transfer coefficients. These coefficients depend on the properties of the solutions and on the hydrodynamic conditions of the system. Such coefficient can either be obtained by experiments or be estimated with the help of empirical correlations of dimensionless numbers. The majority of the correlations referred to in the literamre for various hydrodynamic conditions have the same general form. These include Sherwood number Sh), which contains the mass transfer coefficient, as a function of the Reynolds number Re) and Schmidt number (5c) [89-91]. General mass transfer correlation can be written as... 

The gas flow velocity through the emulsion phase is close to the minimum fluidization velocity When the particles are spherical and have diameters of several tens of microns, this flow condition gives a quite small particle Peclet number, dpUmf/Dc. For example, the Peclet number is estimated as 0.1-0.01 when 122-/Lim-diam. cracking catalyst is fluidized by gas, with Umt = 0.73 cm/sec and Dq = 0.09 cmVsec and it is estimated as 0.001-0.01 for 58-/u.m-diam. particles, with Umt = 0.16 cm/sec. The mechanism of mass transfer between fluid and particles in packed beds is controlled by molecular diffusion under such low Peclet numbers, and the particle Sherwood number kfdp/Dc, is well over 10 (M24). Consequently with intraparticle diffusion shown to be negligible (M21), instantaneous equilibrium is established to be a good approximation [see Eq. (6-24)]. 

The mass transfer coefficient kc is estimated by the correlation of dimensionless j, or Colburn factor, with Sherwood number (Sh), Schmidt number (Sc), and void fraction as described by Cookson (36). 

A slightly different empirical correlation for square microchannels was recently proposed by van Male et al. [89] the correlation leads to an estimated Sherwood number that is about 20% lower than that estimated by Equation (28). 

Usually the entrance region can be neglected in microchannels, and the Sherwood number for fully developed flow can be used for estimating... 

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